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Inverse Problems, ISSN 0266-5611, 01/2019, Volume 35, Issue 3, p. 35004
The primary objective of this research is to investigate an inverse problem of parameter identification in nonlinear mixed quasi-variational inequalities posed... 
nonlinear quasi-variational inequality | obstacle problem | p -Laplacian | inverse problems | regularization | EXISTENCE | MATHEMATICS, APPLIED | p-Laplacian | HEMIVARIATIONAL INEQUALITIES | IDENTIFICATION | PHYSICS, MATHEMATICAL | VALUED EQUILIBRIUM PROBLEMS
Journal Article
Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, 9/2011, Volume 42, Issue 1, pp. 21 - 41
Journal Article
Journal Article
Acta Numerica, ISSN 0962-4929, 05/2012, Volume 21, pp. 89 - 305
In this article we describe recent progress on the design, analysis and implementation of hybrid numerical-asymptotic boundary integral methods for boundary... 
MATHEMATICS | Boundary conditions | Acoustics | Numerical analysis | Asymptotic methods | Scattering | Design engineering | Obstacles | Construction | Asymptotic properties | Integrals | Boundary integral method | Mathematical models
Journal Article
Communications in Partial Differential Equations, ISSN 0360-5302, 10/2010, Volume 35, Issue 11, pp. 2092 - 2122
The fractional Laplacian can be obtained as a Dirichlet-to-Neumann map via an extension problem to the upper half space. In this paper we prove the same type... 
Degenerate Schrödinger equation | Heat semigroup | Fractional Laplacian | Harnack's inequality | Harmonic oscillator | Degenerate schrödinger equation | Fractional laplacian | OBSTACLE PROBLEM | LAPLACIAN | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | Degenerate Schrodinger equation | Partial differential equations | Inequality
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 11/2017, Volume 273, Issue 10, pp. 3061 - 3093
We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff... 
Porous medium equation | Free boundary problems | Tumor growth | Hele–Shaw equation | OBSTACLE PROBLEM | MATHEMATICS | POROUS-MEDIUM EQUATION | REGULARITY | Hele-Shaw equation | MEDIA EQUATION | BOUNDARY | FLOW | Analysis | Tumors | Analysis of PDEs | Mathematics
Journal Article
Inverse Problems, ISSN 0266-5611, 09/2015, Volume 31, Issue 9, pp. 93001 - 93021
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 12/2018, Volume 177, pp. 699 - 732
We deal with a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order s∈(0,1) and summability... 
Integro-differential operators | Nonlocal tail | Fractional Sobolev spaces | OBSTACLE PROBLEM | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | HOLDER CONTINUITY | SUPERHARMONIC FUNCTIONS | PARABOLIC EQUATIONS | INTEGRODIFFERENTIAL OPERATORS | NONLOCAL EQUATIONS | ZYGMUND THEORY | MATHEMATICS | NONLINEAR EQUATIONS | ELLIPTIC-EQUATIONS | Analysis | Differential equations
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 06/2015, Volume 120, pp. 107 - 117
We consider a system of an evolutionary variational inequality of two obstacles type, depending on the temperature, coupled with the heat equation. We prove... 
Variational inequality | Two obstacles | Coupled problem | MATHEMATICS | MATHEMATICS, APPLIED | Obstacles | Nonlinearity | Joining | Evolutionary | Inequalities | Heat equations
Journal Article
Mathematics and Mechanics of Solids, ISSN 1081-2865, 5/2019, Volume 24, Issue 5, pp. 1503 - 1529
Our objective is to identify two-dimensional equations that model an obstacle problem for a linearly elastic elliptic membrane shell subjected to a confinement... 
asymptotic analysis | Obstacle problems | variational inequalities | elliptic membrane shells | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MATERIALS SCIENCE, MULTIDISCIPLINARY | MATHEMATICAL JUSTIFICATION | Mathematical Physics | Analysis of PDEs | Mathematics
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 2, pp. A918 - A945
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2016, Volume 307, pp. 183 - 203
Efficient computational models that retain essential physics of the associated continuous mathematical models are important for several applications including... 
Finite element method | Spectral Nyström boundary element method | Wave propagation | Horn problem | High-order | Interface | Spectral Nystrom boundary element method | MATHEMATICS, APPLIED | OPTIMIZATION | Models | Numerical analysis | Algorithms | Radiation | Obstacles | Computer simulation | Computation | Media | Horns | Mathematical models
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 07/2017, Volume 34, Issue 4, pp. 899 - 932
We study the two membranes problem for different operators, possibly nonlocal. We prove a general result about the Hölder continuity of the solutions and we... 
Regularity | Fractional operators | Obstacle problem | MATHEMATICS, APPLIED | ELLIPTIC-EQUATIONS | REGULARITY THEORY
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 3, pp. 1879 - 1905
Journal Article
Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 2/2010, Volume 195, Issue 2, pp. 533 - 560
Journal Article
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, ISSN 0926-6003, 06/2018, Volume 70, Issue 2, pp. 531 - 569
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 04/2018, Volume 75, Issue 7, pp. 2311 - 2327
Journal Article